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Proof step 6 from proof sym (previous step)

disj(a ' + x0, y), a ∈ y, ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ disj(x, y) → (disj(a ' + x, y) ↔ ¬ a ∈ y)
Proof step 8:
disj(a ' + x0, y), a ∈ y, ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0), disj(x0, y)

Rule argument

spec: <toplevel> name: cons-01 seq: ⊦ disj(x, y) → (disj(a ' + x, y) ↔ ¬ a ∈ y) subst: [y, x, a] → [y, x0, a] flags: <all paths>

Additional information

Used terms: y, x0, a